Vertical motion with constant acceleration

[Kajayacht]

Homework Statement

A research balloon of total mass 410 kg is descending vertically with a downward acceleration of 1.0 m/s2. How much ballast must be thrown from the car to give the balloon an upward acceleration equal to 1.6 m/s2, presuming that the upward lift of the balloon does not change.

Homework Equations

B-w=m*a
w=mg

The Attempt at a Solution

w= 410*9.8
w= 4018 N

B-4018 = 410*-1
B=3608

3608-m{2}*9.8= m{2}*1.6
2255= m{2}+9.8m{2}
2255= 10.8m{2}
m{2} = 208.80
410-208.80= 201.2kg

 

[PhanthomJay]

Homework Statement

A research balloon of total mass 410 kg is descending vertically with a downward acceleration of 1.0 m/s2. How much ballast must be thrown from the car to give the balloon an upward acceleration equal to 1.6 m/s2, presuming that the upward lift of the balloon does not change.

Homework Equations

B-w=m*a
w=mg

The Attempt at a Solution

w= 410*9.8
w= 4018 N

B-4018 = 410*-1
B=3608

3608-m{2}*9.8= m{2}*1.6
2255= m{2}+9.8m{2}your algebra is wrong. Should be 3608 = 11.4m{2}
2255= 10.8m{2}
m{2} = 208.80
410-208.80= 201.2kg

Your method is good. Check your math error as noted above.

 

[baba89]

of ballast must be thrown from the car to give the balloon an upward acceleration equal to 1.6 m/s2.

I would like to clarify that the equations and calculations used in the attempt to solve this problem are correct. However, it is important to note that the given scenario is simplified and does not take into account factors such as air resistance and the changing upward lift of the balloon as ballast is thrown. In a real-life situation, these factors would need to be considered in order to accurately determine the amount of ballast needed for the desired upward acceleration. Additionally, it would be helpful to provide more context and information about the research balloon and its surroundings in order to fully understand and analyze the situation.